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href="/" title="首页" class="iconfont icon-home router-link-active" data-v-06225672></a></li> <li data-v-06225672><a href="/algor/#算法" data-v-06225672>算法</a></li><li data-v-06225672><a href="/algor/#算法训练营" data-v-06225672>算法训练营</a></li></ul> <div class="info" data-v-06225672><div title="作者" class="author iconfont icon-touxiang" data-v-06225672><a href="https://github.com/linxin1123" target="_blank" title="作者" class="beLink" data-v-06225672>lingxin</a></div> <div title="创建时间" class="date iconfont icon-riqi" data-v-06225672><a href="javascript:;" data-v-06225672>2023-02-17</a></div> <!----></div></div></div> <!----> <div class="content-wrapper"><div class="right-menu-wrapper"><div class="right-menu-margin"><div class="right-menu-title">目录</div> <div class="right-menu-content"></div></div></div> <h1><img src="">二叉搜索树<!----></h1>  <div class="theme-vdoing-content content__default"><h2 id="二叉搜索树"><a href="#二叉搜索树" class="header-anchor">#</a> 二叉搜索树</h2> <h3 id="_1-定义"><a href="#_1-定义" class="header-anchor">#</a> 1. 定义</h3> <ul><li>左子树小于根节点</li> <li>右子树大于根节点</li></ul> <h3 id="_2-求某个节点的后继"><a href="#_2-求某个节点的后继" class="header-anchor">#</a> 2. 求某个节点的后继</h3> <h4 id="概念-比当前节点大的最小节点"><a href="#概念-比当前节点大的最小节点" class="header-anchor">#</a> 概念：比当前节点大的最小节点</h4> <ul><li>节点存在右子树
<ul><li>先找到右子树</li> <li>一路往左走，直到空树</li></ul></li> <li>节点不存在右子树
<ul><li>后继可能存在于查找到改节点的路上</li></ul></li></ul> <h3 id="_3-求节点的前驱"><a href="#_3-求节点的前驱" class="header-anchor">#</a> 3. 求节点的前驱</h3> <ul><li>比当前节点小的最大节点</li> <li>节点存在左子树
<ul><li>先找到左子树</li> <li>一路往右子树走，直到为空</li></ul></li> <li>节点不存在左子树
<ul><li>前驱可能存在查找该节点的路上</li></ul></li></ul> <h3 id="_4-删除节点"><a href="#_4-删除节点" class="header-anchor">#</a> 4. 删除节点</h3> <ul><li>分为三种情况
<ul><li>该节点只有左子树，直接拼接左子树</li> <li>该节点只有右子树，直接拼接右子树</li> <li>存在左右子树
<ul><li>求该节点的的后继</li> <li>该节点的值与其后继的值交换</li> <li>删除后继（==因为后继是右子树一路往左，这样删除后继是，后继最多只存在右子树，所以回到上述前两种情况==）</li></ul></li></ul></li></ul> <h2 id="leetcode"><a href="#leetcode" class="header-anchor">#</a> LeetCode</h2> <h4 id="_701-二叉搜索树中的插入操作-二叉搜索树查找插入模板"><a href="#_701-二叉搜索树中的插入操作-二叉搜索树查找插入模板" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/insert-into-a-binary-search-tree/" target="_blank" rel="noopener noreferrer">701. 二叉搜索树中的插入操作(二叉搜索树查找插入模板)<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给定二叉搜索树（BST）的根节点 <code>root</code> 和要插入树中的值 <code>value</code> ，将值插入二叉搜索树。 返回插入后二叉搜索树的根节点。 输入数据 <strong>保证</strong> ，新值和原始二叉搜索树中的任意节点值都不同。</p> <p><strong>注意</strong>，可能存在多种有效的插入方式，只要树在插入后仍保持为二叉搜索树即可。 你可以返回 <strong>任意有效的结果</strong> 。</p> <p><strong>示例 1：</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/10/05/insertbst.jpg" alt="img"></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：root = [4,2,7,1,3], val = 5
输出：[4,2,7,1,3,5]
解释：另一个满足题目要求可以通过的树是：
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><p><strong>示例 2：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：root = [40,20,60,10,30,50,70], val = 25
输出：[40,20,60,10,30,50,70,null,null,25]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>示例 3：</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：root = [4,2,7,1,3,null,null,null,null,null,null], val = 5
输出：[4,2,7,1,3,5]
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示：</strong></p> <ul><li>树中的节点数将在 <code>[0, 104]</code>的范围内。</li> <li><code>-108 &lt;= Node.val &lt;= 108</code></li> <li>所有值 <code>Node.val</code> 是 <strong>独一无二</strong> 的。</li> <li><code>-108 &lt;= val &lt;= 108</code></li> <li><strong>保证</strong> <code>val</code> 在原始BST中不存在。</li></ul> <h5 id="完整代码"><a href="#完整代码" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */</span>
<span class="token comment">/**
 * @param {TreeNode} root
 * @param {number} val
 * @return {TreeNode}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">insertIntoBST</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">root<span class="token punctuation">,</span> val</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>root<span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">return</span> <span class="token keyword">new</span> <span class="token class-name">TreeNode</span><span class="token punctuation">(</span>val<span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    <span class="token comment">//  更好的一种写法，可能不好理解</span>

    <span class="token keyword">if</span><span class="token punctuation">(</span>val<span class="token operator">&lt;</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span><span class="token punctuation">{</span>
        root<span class="token punctuation">.</span>left<span class="token operator">=</span><span class="token function">insertIntoBST</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">,</span>val<span class="token punctuation">)</span>
    <span class="token punctuation">}</span><span class="token keyword">else</span><span class="token punctuation">{</span>
        root<span class="token punctuation">.</span>right<span class="token operator">=</span><span class="token function">insertIntoBST</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">,</span>val<span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    <span class="token keyword">return</span> root

<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br></div></div><h4 id="二叉搜索树寻找后继模板"><a href="#二叉搜索树寻找后继模板" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/successor-lcci/" target="_blank" rel="noopener noreferrer">二叉搜索树寻找后继模板<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>设计一个算法，找出二叉搜索树中指定节点的“下一个”节点（也即中序后继）。</p> <p>如果指定节点没有对应的“下一个”节点，则返回<code>null</code>。</p> <p><strong>示例 1:</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入: root = [2,1,3], p = 1

  2
 / \
1   3

输出: 2
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br></div></div><p><strong>示例 2:</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入: root = [5,3,6,2,4,null,null,1], p = 6

      5
     / \
    3   6
   / \
  2   4
 /   
1

输出: null
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br></div></div><h5 id="完整代码-2"><a href="#完整代码-2" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */</span>
<span class="token comment">/**
 * @param {TreeNode} root
 * @param {TreeNode} p
 * @return {TreeNode}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">inorderSuccessor</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">root<span class="token punctuation">,</span> p</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 即找出二叉搜索树的后继</span>

    <span class="token comment">// 即比当前节点大的最小节点</span>

    <span class="token comment">// 如果存在右子树，先右子树，然后一路往左走</span>

    <span class="token comment">// 1.如果不存在右子树，则后继节点可能在祖先</span>

    <span class="token comment">// 2.从根节点开始查找，如果往左走，说明查找的节点在左边，那么当前节点是不是比目标节点大</span>

    <span class="token comment">// 3.所有只要往左走，我们就记录当前节点，因为它比目标节点大，且很靠经目标节点</span>

    <span class="token keyword">let</span> res<span class="token operator">=</span><span class="token keyword">null</span>

    <span class="token keyword">const</span> <span class="token function-variable function">search</span><span class="token operator">=</span><span class="token punctuation">(</span><span class="token parameter">root<span class="token punctuation">,</span>p</span><span class="token punctuation">)</span><span class="token operator">=&gt;</span><span class="token punctuation">{</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>p<span class="token punctuation">.</span>val<span class="token operator">&gt;</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token function">search</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">,</span>p<span class="token punctuation">)</span>
        <span class="token punctuation">}</span><span class="token keyword">else</span> <span class="token keyword">if</span><span class="token punctuation">(</span>p<span class="token punctuation">.</span>val<span class="token operator">&lt;</span>root<span class="token punctuation">.</span>val<span class="token punctuation">)</span><span class="token punctuation">{</span>
            res<span class="token operator">=</span>root
            <span class="token function">search</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">,</span>p<span class="token punctuation">)</span>
        <span class="token punctuation">}</span><span class="token keyword">else</span><span class="token punctuation">{</span>
            <span class="token comment">// 相等</span>
            <span class="token comment">// 判断是否有右子树</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>root<span class="token punctuation">.</span>right<span class="token punctuation">)</span> <span class="token keyword">return</span> 

            <span class="token comment">// 存在</span>
            <span class="token comment">// 找到右子树，一路左走</span>
            <span class="token keyword">let</span> node<span class="token operator">=</span>root<span class="token punctuation">.</span>right
            <span class="token keyword">while</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>left<span class="token operator">!=</span><span class="token keyword">null</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
                node<span class="token operator">=</span>node<span class="token punctuation">.</span>left
            <span class="token punctuation">}</span>
            res<span class="token operator">=</span>node
        <span class="token punctuation">}</span>
    <span class="token punctuation">}</span>

    <span class="token function">search</span><span class="token punctuation">(</span>root<span class="token punctuation">,</span>p<span class="token punctuation">)</span>   
    <span class="token keyword">return</span> res

<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br><span class="line-number">48</span><br><span class="line-number">49</span><br><span class="line-number">50</span><br><span class="line-number">51</span><br><span class="line-number">52</span><br><span class="line-number">53</span><br></div></div><h4 id="_450-删除二叉搜索树中的节点模板"><a href="#_450-删除二叉搜索树中的节点模板" class="header-anchor">#</a> <a href="https://leetcode.cn/problems/delete-node-in-a-bst/" target="_blank" rel="noopener noreferrer">450. 删除二叉搜索树中的节点模板<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></h4> <p>给定一个二叉搜索树的根节点 <strong>root</strong> 和一个值 <strong>key</strong>，删除二叉搜索树中的 <strong>key</strong> 对应的节点，并保证二叉搜索树的性质不变。返回二叉搜索树（有可能被更新）的根节点的引用。</p> <p>一般来说，删除节点可分为两个步骤：</p> <ol><li>首先找到需要删除的节点；</li> <li>如果找到了，删除它。</li></ol> <p><strong>示例 1:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/09/04/del_node_1.jpg" alt="img"></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入：root = [5,3,6,2,4,null,7], key = 3
输出：[5,4,6,2,null,null,7]
解释：给定需要删除的节点值是 3，所以我们首先找到 3 这个节点，然后删除它。
一个正确的答案是 [5,4,6,2,null,null,7], 如下图所示。
另一个正确答案是 [5,2,6,null,4,null,7]。
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div><p><strong>示例 2:</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入: root = [5,3,6,2,4,null,7], key = 0
输出: [5,3,6,2,4,null,7]
解释: 二叉树不包含值为 0 的节点
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br></div></div><p><strong>示例 3:</strong></p> <div class="language- line-numbers-mode"><pre class="language-text"><code>输入: root = [], key = 0
输出: []
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br></div></div><p><strong>提示:</strong></p> <ul><li>节点数的范围 <code>[0, 104]</code>.</li> <li><code>-105 &lt;= Node.val &lt;= 105</code></li> <li>节点值唯一</li> <li><code>root</code> 是合法的二叉搜索树</li> <li><code>-105 &lt;= key &lt;= 105</code></li></ul> <p><strong>进阶：</strong> 要求算法时间复杂度为 O(h)，h 为树的高度。</p> <h5 id="完整代码-3"><a href="#完整代码-3" class="header-anchor">#</a> 完整代码</h5> <div class="language-js line-numbers-mode"><pre class="language-js"><code><span class="token comment">/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */</span>
<span class="token comment">/**
 * @param {TreeNode} root
 * @param {number} key
 * @return {TreeNode}
 */</span>
<span class="token keyword">var</span> <span class="token function-variable function">deleteNode</span> <span class="token operator">=</span> <span class="token keyword">function</span><span class="token punctuation">(</span><span class="token parameter">root<span class="token punctuation">,</span> key</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment">// 更简洁的一种写法，比较难懂</span>

    <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>root<span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token keyword">null</span>

    <span class="token comment">// 找到，分三种情况，只有左子树，只要右子树，左右子树都有</span>

    <span class="token keyword">if</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>val<span class="token operator">===</span>key<span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token operator">===</span><span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token keyword">return</span> root<span class="token punctuation">.</span>right
        <span class="token keyword">if</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token operator">===</span><span class="token keyword">null</span><span class="token punctuation">)</span> <span class="token keyword">return</span> root<span class="token punctuation">.</span>left


        <span class="token comment">// 左右子树都存在</span>
        <span class="token keyword">let</span> next<span class="token operator">=</span>root<span class="token punctuation">.</span>right
        
        <span class="token comment">// 一路向左找到后继</span>
        <span class="token keyword">while</span><span class="token punctuation">(</span>next<span class="token punctuation">.</span>left<span class="token punctuation">)</span><span class="token punctuation">{</span>
            next<span class="token operator">=</span>next<span class="token punctuation">.</span>left
        <span class="token punctuation">}</span>

        <span class="token comment">// 删除后继</span>
        <span class="token comment">// 在后继树中删除next节点</span>
        root<span class="token punctuation">.</span>right<span class="token operator">=</span><span class="token function">deleteNode</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">,</span>next<span class="token punctuation">.</span>val<span class="token punctuation">)</span>
        root<span class="token punctuation">.</span>val<span class="token operator">=</span>next<span class="token punctuation">.</span>val
        <span class="token keyword">return</span> root
    <span class="token punctuation">}</span>


    <span class="token keyword">if</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>val<span class="token operator">&lt;</span>key<span class="token punctuation">)</span><span class="token punctuation">{</span>
        root<span class="token punctuation">.</span>right<span class="token operator">=</span><span class="token function">deleteNode</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>right<span class="token punctuation">,</span>key<span class="token punctuation">)</span>
    <span class="token punctuation">}</span><span class="token keyword">else</span><span class="token punctuation">{</span>
        root<span class="token punctuation">.</span>left<span class="token operator">=</span><span class="token function">deleteNode</span><span class="token punctuation">(</span>root<span class="token punctuation">.</span>left<span class="token punctuation">,</span>key<span class="token punctuation">)</span>
    <span class="token punctuation">}</span>

    <span class="token keyword">return</span> root

<span class="token punctuation">}</span><span class="token punctuation">;</span>
</code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br><span class="line-number">25</span><br><span class="line-number">26</span><br><span class="line-number">27</span><br><span class="line-number">28</span><br><span class="line-number">29</span><br><span class="line-number">30</span><br><span class="line-number">31</span><br><span class="line-number">32</span><br><span class="line-number">33</span><br><span class="line-number">34</span><br><span class="line-number">35</span><br><span class="line-number">36</span><br><span class="line-number">37</span><br><span class="line-number">38</span><br><span class="line-number">39</span><br><span class="line-number">40</span><br><span class="line-number">41</span><br><span class="line-number">42</span><br><span class="line-number">43</span><br><span class="line-number">44</span><br><span class="line-number">45</span><br><span class="line-number">46</span><br><span class="line-number">47</span><br><span class="line-number">48</span><br><span class="line-number">49</span><br><span class="line-number">50</span><br><span class="line-number">51</span><br></div></div></div></div>  <div class="page-edit"><div class="edit-link"><a href="https://github.com/linxin1123/vuepress-blog/edit/master/docs/07.算法/41.算法训练营/10.二叉搜索树.md" target="_blank" rel="noopener noreferrer">编辑</a> <span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></div> <!----> <div class="last-updated"><span class="prefix">上次更新:</span> <span class="time">2023/02/17, 11:29:32</span></div></div> <div class="page-nav-wapper"><div class="page-nav-centre-wrap"><a href="/pages/3fd3d8/" class="page-nav-centre page-nav-centre-prev"><div class="tooltip">树与图-cnblog</div></a> <a href="/pages/cf81aa/" class="page-nav-centre page-nav-centre-next"><div class="tooltip">二叉堆</div></a></div> <div class="page-nav"><p class="inner"><span class="prev">
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